Second moment (integral)

Form a double integral to represent the area of the plane figure bounded by the polar curve $r=3+2\cos\theta$ and the radius vectors at $\theta=0$ and $\theta=\pi/2$, and evaluate it.

For a region given in polar form with boundary $r=f(\theta)$, the inner limits of $\displaystyle\int\int r\,dr\,d\theta$ for the area are typically:

Once the area $A$ and the first moment $M_{OA}$ about line $OA$ of a polar region are both known, the centroid's perpendicular distance $h$ from $OA$ is found by: